# Information Content and Maximum Entropy of Compartmental Systems in Equilibrium

## TL;DR

This paper introduces an information-theoretic framework to analyze equilibrium compartmental systems, enabling model selection and revealing structural properties.

## Contribution

The novel contribution is extending the maximum entropy principle to compartmental dynamics and deriving path entropy and entropy rates for such systems.

## Key findings

- Closed-form expressions for path entropy and entropy rates are derived in equilibrium.
- The framework reveals hidden structural properties of complex systems like the global carbon cycle.
- It provides a systematic approach to address equifinality in model selection.

## Abstract

Mass-balanced compartmental systems defy classical deterministic entropy measures since both metric and topological entropy vanish in dissipative dynamics. By interpreting open compartmental systems as absorbing continuous-time Markov chains that describe the random journey of a single representative particle, we allow established information-theoretic principles to be applied to this particular type of deterministic dynamical system. In particular, path entropy quantifies the uncertainty of complete trajectories, while entropy rates measure the average uncertainty of instantaneous transitions. Using Shannon’s information entropy, we derive closed-form expressions for these quantities in equilibrium and extend the maximum entropy principle (MaxEnt) to the problem of model selection in compartmental dynamics. This information-theoretic framework not only provides a systematic way to address equifinality but also reveals hidden structural properties of complex systems such as the global carbon cycle.